We propose to develop new statistical methods for improving analyses of multivariate, longitudinal and functional data from biomedical studies. There is increasing concern that exposures occurring during critical windows can lead to later adverse health effects, motivating prospective studies collecting detailed data on multiple time-varying exposures and health outcomes. New statistical methods are needed to efficiently discover critical windows and time-varying dependencies in such high-dimensional data sets, while limiting false discoveries. These methods may lead to fundamental new insights into mechanisms by which exposures induce adverse health effects, while also allowing for the development of targeted interventions and more accurate predictions of disease risk. Our goals include the following. 1. Develop nonparametric Bayes statistical methods for flexibly characterizing differences among individuals in functional data, such as trajectories over time in oxidative stress, reproductive hormones, nutrients and pregnancy weight. 2. Develop methods for flexibly predicting a health response based on multiple time- varying factors, while also estimating critical windows and discovering dynamic relationships between the different factors. 3. Apply these methods to assess relationships between oxidative stress, nutrients and reproductive hormones over the menstrual cycle accounting for the role of age, obesity and smoking. Also consider applications to identify patterns of pregnancy weight gain associated with short-term infant health outcomes.